# Finding the radius of a brass ball using tension?

• rought
In summary, to find the radius of the brass ball attached to a wire with a tension of 120N, you need to first find the mass of the ball by balancing the tension with the weight force. Then, you can use the formula for the volume of a sphere (V = (4/3)πR^3) to calculate the radius from the mass.
rought

## Homework Statement

One end of a wire is attached to a ceiling and a solid brass ball is tied to the lower end. The tension in the wire is 120N what is the radius of the brass ball.

## Homework Equations

Brass Mass Density (kg/m^3) = 80470

I have no clue how to solve this one, can anyone help?

Start by drawing a free body diagram. You need to figure out the mass of the ball. How do you think you might do that?

hage567 said:
Start by drawing a free body diagram. You need to figure out the mass of the ball. How do you think you might do that?

Could you find the mass of the ball by taking the tension and dividing it by the force of gravity? Would tension equal the weight force (Mass x Gravity) ?

rought said:
Could you find the mass of the ball by taking the tension and dividing it by the force of gravity? Would tension equal the weight force (Mass x Gravity) ?
That's correct. Two forces act on the ball: The upward tension of the wire and the downward pull of gravity. They must balance, thus: T = mg.

Doc Al said:
That's correct. Two forces act on the ball: The upward tension of the wire and the downward pull of gravity. They must balance, thus: T = mg.

Ok I got that, but how do you find the radius of the ball from the volume that I calculated from the mass?

What's the formula for the volume of a sphere?

hage567 said:
What's the formula for the volume of a sphere?

V = (4/3)πR^3 right?

That's right.

hage567 said:
That's right.

Alrite I get what to do now, thanks a ton =]

You're welcome.

## 1. What is the purpose of finding the radius of a brass ball using tension?

The purpose of finding the radius of a brass ball using tension is to determine the size of the ball, which can be useful in various experiments or applications such as measuring its volume or calculating its buoyancy.

## 2. What is the process for finding the radius of a brass ball using tension?

The process for finding the radius of a brass ball using tension involves suspending the ball from a string and measuring the tension in the string. By using the tension, along with the weight of the ball and the gravitational constant, the radius of the ball can be calculated.

## 3. Can the radius of a brass ball be accurately measured using tension?

Yes, the radius of a brass ball can be accurately measured using tension as long as the measurements are taken carefully and accurately. It is important to use the correct formula and to ensure that the ball is hanging freely and not touching any other surfaces.

## 4. Are there any limitations or factors that may affect the accuracy of this method?

Yes, there are some limitations and factors that may affect the accuracy of finding the radius of a brass ball using tension. These include the accuracy of the measurements taken, the precision of the equipment used, and external factors such as air resistance or friction on the string.

## 5. Is there any other method for determining the radius of a brass ball?

Yes, there are other methods for determining the radius of a brass ball, such as using a caliper or ruler to directly measure the diameter of the ball. Another method is to submerge the ball in water and measure the displacement, which can then be used to calculate its volume and subsequently the radius.

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